99191 - Devices, Circuits and Algorithms for Quantum Computing M

Learning outcomes

The course introduces the fundamental concepts for understanding the hardware and software systems underlying quantum computing. Upon completion, the student masters the principles underlying quantum computation, an understanding of the quantum circuit model, the main algorithms, the physical concepts underlying the implementation of hardware systems, and the main electronic architectures.

Course contents

The course is divided into two modules. The first module introduces the formalism at the basis of the description of quantum systems, the  concepts of qubit and quantum circuit, together with the operations that define quantum algorithms starting from the composition of fundamental gates. Computer exercises are also planned aimed at the simulation of elementary quantum circuits (phase kick-back, Bell states) and the implementation of some algorithms (Grover, QFT, VQE).

In the second module, the physical principles underlying the realization and operation of qubits are introduced and the physical behaviour of fundamental quantum gates is analysed, with particular reference to solutions based on superconducting circuits. The module is complemented with computer exercises with QuTiP aimed at illustrating the main concepts and simulating the behaviour of some quantum gates.

First module

• The computer as a physical system. Limitations of classical computers. What is a quantum computer. Limitations of classical paradigm. What is a qubit and its representation with the Bloch sphere. Classical and quantum complexity. Quantum advantage. State of the art: NISQ and FTQC.
• Dirac formalism and quantum representation of information. Hilbert spaces: operators and their matrix representation. Tensor product. Composite systems: separable and entangled states. Superposition, entanglement, interference. Measure.
• Reversibility, unitary transformations and quantum gates. No-cloning theorem.
• Quantum circuits. 1- and 2-qubit gates. Bell states, teleportation. Rotation operators. Universality. Examples of circuit decomposition, transpilation and mapping.
• Interference amd phase kick-back as fundamental mechanisms of quantum algorithms. The concept of oracle. Deutsch and Grover algorithms. Quantum Fourier Transform (QFT) and Quantum Phase Estimation (QPE).
• Elementary algorithmic models for noise; bit-flip and phase-flip codes. The concept of logic qubit.
• Exploitation of present hardware: the variational paradigm and the VQE example.

Second module

• Review on the postulates of Quantum Mechanics: quantization, commutator of conjugate operators, Schroedinger equation, measures of observables and probabilistic interpretation, Heisenberg's uncertainty principle, time-dependent Schroedinger equation, evolution operator. Schroedinger, Heisenberg and interaction pictures.
• Harmonic oscillator: quantization and energy levels. Creation and annihilation operators and their properties.
• Brief phenomenological introduction to superconductivity. Notes on the Ginzburg-Landau theory. Josephson junction: fundamental relationships between current, voltage and phase.
• Superconductor qubits. The quantum LC oscillator. The transmon qubit: structure, Hamiltonian and analysis of the energy levels. Flux-tuning transmon.
• Noise and decoherence in qubits: models (outline) and characterization techniques, common sources of noise, techniques to mitigate their impact.
• Single qubit gates: qubit control and dynamics, Rabi frequency. Virtual Z-gate. Advanced qubit control techniques to reduce leakage and phase errors (outline).
• Two qubits/resonators systems: Hamiltonian analysis and related simplifications, dispersive regime. Coupling between two transmons.
• 2-qubit gates: example implementation of iSWAP and CPHASE gates.
• Qubit readout: general problems, dispersive readout.
  

 

Readings/Bibliography

1. Daniel D. Stancil, Gregory T. Bird, “Principles of Superconducting Quantum Computers”, Wiley, 2022
2. Ray LaPierre, “Introduction to Quantum Computing”, Springer Cham, 2021
3. Michael A. Nielsen, Isaac L. Chuang, "Quantum Computation and Quantum Information", Cambridge University Press, 2010

Teaching methods

Lectures supplemented by computer exercises.

Assessment methods

The exam consists of an oral interview on the topics covered in both teaching modules. Not only the student's critical ability in connecting different parts of the program and to justify reasoning will be evaluated, but also the possible presence of training gaps or the use of inappropriate language. The final grade expresses the evaluation of the mastery of the concepts and the critical capacity shown by the student.

Teaching tools

Slides, documentation provided by teachers on specific topics, multimedia material.

Office hours

See the website of Antonio Gnudi

See the website of Nicolò Attilio Speciale